It is only recently that simulation has begun to play an important role in pricing high-dimensional American options. This was due to the fact that since Monte Carlo simulation generally works forward in time while dynamic programming works backwards, it was generally believed that the two were somewhat incompatible. Research in recent years has shown that this is not the case and that Monte Ca...

Option pricing is the the core content of modern finance. American option is widely accepted by investors for its flexibility of exercising time. In this paper, American option pricing formula is calculated for uncertain financial market and some mathematical properties of them are discussed. In addition, some examples are proposed. keywords: finance, uncertain process, option pricing

The Black–Scholes Option pricing model (OPM) developed in 1973 has always been taken as the cornerstone of option pricing model. The generic applications of such a model are always restricted by its nature of not being suitable for fuzzy environment since the decision-making problems occurring in the area of option pricing are always with a feature of uncertainty. When an investor faces an opti...

This paper considers the pricing of multiple exercise options in discrete time. This type of option can be exercised up to a fixed finite number of times over the lifetime of the contract. We allow multiple exercise of the option at each time point up to a constraint, a feature relevant for pricing swing options in energy markets. It is shown that, in the case where an option can be exercised a...

Pricing financial options often requires Monte Carlo methods. One particular case is that of barrier options, whose payoff may be zero depending on whether or not an underlying asset crosses a barrier during the life of the option. This paper develops variance reduction techniques that take advantage of the special structure of barrier options, and are appropriate for general simulation problem...

The central part of pricing agricultural commodity futures options is to find appropriate stochastic process of the underlying assets. The Black’s (1976) futures option pricing model laid the foundation for a new era of futures option valuation theory. The geometric Brownian motion assumption girding the Black’s model, however, has been regarded as unrealistic in numerous empirical studies. Opt...

Options pricing model parameters are inherently imprecise due to fluctuations in the real-world financial market. Traditional option pricing methods do not account for the uncertainty in parameters, but the fuzzy set theory may be applicable. This paper proposes a cash-or-nothing European call binary option pricing model based on the hypothesis that the underlying asset price, risk-free rate of...

We propose a neural network approach to price EU call options that significantly outperforms some existing pricing models and comes with guarantees that its predictions are economically reasonable. To achieve this, we introduce a class of gated neural networks that automatically learn to divide-and-conquer the problem space for robust and accurate pricing. We then derive instantiations of these...